Ted Cruz’s decision to pick Carly Fiorina as his running mate kicked off the veepstakes season earlier than expected. But three months before the conventions, all the remaining candidates with a chance at their party’s nomination should be working on their vice-presidential selections.

Why? After all, running mates in the general election have a limited impact. There’s no evidence they provide demographic help. (Picking a woman hasn’t helped pick up votes from women, for example, no matter what Cruz was thinking when he chose Fiorina.) Nor has a presidential candidate ever successfully established his own story line through his choice of a No. 2.

The one way running mates might help is in their home states. Even here the evidence is mixed. The ticket gets about a 3 percent boost for the VP’s home state (everything else being constant), according to research by Boris Heersink and Brenton Peterson. Yes, that could matter in a close overall contest. But others dispute that finding. The effect only turns up in small states, say Christopher J. Devine and Kyle C. Kopko, and then only when the veepstakes winner is a longtime local fixture, such as Joe Biden in Delaware.

The reason the presidential front-runners should be paying attention to their decision is that quite a few vice-presidential picks have proved troublesome. Richard Nixon in 1952, Thomas Eagleton in 1972, Geraldine Ferraro in 1984, Dan Quayle in 1988 and Sarah Palin in 2008 all had problems that put them in danger of being dropped from the ticket. (Eagleton was replaced.)

What each of those choices had in common was that none of them had been vetted by having run in a national campaign before. Ideally, the running mate will have had this experience, as George H.W. Bush, Al Gore and Biden all had before they were selected for the No. 2 spot by Ronald Reagan, Bill Clinton and Barack Obama, respectively.

The running mate should also be someone the nominee is prepared to have in his or her administration. Vice presidents aren’t easily fired, although the amount of responsibility they have is entirely up to the president. Someone who has no record as a team player is unlikely to be chosen. But no one wants someone who will be useless in the job either, as long as there’s no electoral effect.

Unfortunately for Hillary Clinton, the Democrats right now have no one who fits the bill perfectly. She can find a swing-state senator such as Virginia’s Tim Kaine, but not one who has been though the gauntlet of running for president.

The Republicans have a different challenge. Under other circumstances they would seem to have a wealth of options who cover many bases: Marco Rubio, John Kasich or Scott Walker, for example -- a swing-state bonanza. A normal nominee could pick any of them. Trump, however, may be limited in his choices, just as George McGovern was before his disastrous selection of Eagleton. Strategic politicians will be reluctant to join a likely loser -- especially one many Republican party actors don’t approve of.

In an ideal world, the remaining presidential candidates would not only be thinking about their vice-presidential choices. It’s not too soon to think about the transition after the general election too.

George W. Bush’s administration by all accounts did a good job of passing the presidency to Obama, and Obama reportedly wants to do the same for his successor. New laws make it an obligation for the outgoing administration to cooperate in any case, but no one can force the candidates to participate.

It would be a surprise if Clinton wasn’t already looking beyond November. Trump? As much as much of the Republican establishment doesn’t even want to consider the possibility of his election, let alone his presidency, it should be more worried if he’s not preparing for it.

And then there’s the example of Spiro Agnew, who survived two elections, in 1968 and 1972, only to have to resign from office as part of a plea bargain (though Agnew turned out to be one of Nixon's lesser mistakes). It’s hard to prove that such selections caused damage but no nominee wants media attention focused on a running mate's baggage or shortcomings.

This column does not necessarily reflect the opinion of the editorial board or Bloomberg LP and its owners.